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Axions and axion-like particles (ALPs) are some of the best-motivated dark matter (DM) candidates. Under certain circumstances, large axion fluctuations in the early universe can collapse to form dense configurations called axion clumps. The densest axion clumps are metastable states known as oscillons. In this paper we propose a new class of observables that exploit the axion's coupling to photons. As a result of this coupling an axion clump acts like an inhomogeneous refractive optical medium -- a lens -- that causes anomalous dispersion of incident electromagnetic waves. The dispersion of electromagnetic waves by axion clumps clearly distinguishes this lensing effect from gravitational lensing. Axion clumps passing in front of background radio sources act as lenses and lead to apparent positional shifts that can potentially be discovered by high-precision radio astrometry missions with the forthcoming Square Kilometer Array (SKA). We discuss the sensitivity of SKA to lensing effects in a variety of axion halo models. While gravitational microlensing surveys have placed strong constraints on the amount of DM that exists in the form of non-luminous astrophysical objects they have been unable to do so for objects in the mass range $[10^{-14}, 10^{-11}] M_\odot$. We find that, over a wide range of parameter space, SKA will be sensitive to optical lensing by oscillons in the mass range that is currently unconstrained by microlensing surveys.